(7x-23)(3x-17)=180

Solution for (7x-23)(3x-17)=180 equation:

(7x-23)(3x-17)=180

We move all terms to the left:

(7x-23)(3x-17)-(180)=0

We multiply parentheses ..

(+21x^2-119x-69x+391)-180=0

We get rid of parentheses

21x^2-119x-69x+391-180=0

We add all the numbers together, and all the variables

21x^2-188x+211=0

a = 21; b = -188; c = +211;
Δ = b2-4ac
Δ = -1882-4·21·211
Δ = 17620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17620}=\sqrt{4*4405}=\sqrt{4}*\sqrt{4405}=2\sqrt{4405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-188)-2\sqrt{4405}}{2*21}=\frac{188-2\sqrt{4405}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-188)+2\sqrt{4405}}{2*21}=\frac{188+2\sqrt{4405}}{42}
$